Multi-transmitter channel estimation for a time varying channel

ABSTRACT

Disclosed is a method, receiver, multi-receiver device, system and computer readable medium for configuring a receiver to perform multi-transmitter channel estimation for a time-varying channel. In one aspect, the method includes: wirelessly receiving at least two frames, each frame including a block of training symbols received at different points in time for a time-varying channel; estimating, for each block at a block location, a first channel coefficient of the time-varying channel, wherein the block location is the same for each block; and interpolating or extrapolating a plurality of second channel coefficients for the respective training symbols of each block based on the respective first channel coefficient.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority from Australian ProvisionalPatent Application No. 2016901120 filed on 24 Mar. 2016, the contents ofwhich is incorporated herein by reference.

TECHNICAL FIELD

The present invention relates generally to wireless communication and,in particular to channel estimation for a time varying channel.

BACKGROUND

The application of technology known as multiple-input multiple-output(MIMO) has become prevalent for wireless communication in recent years.MIMO uses multiple transmitters and multiple receivers all operating inthe same radio frequency. Modern wireless standards such as Long TermEvolution Advanced (LTE-Advanced) mobile standard and IEEE 802.11acwireless local area network standard define the use of eight or moretransmitters for the purpose of MIMO wireless communication.

Typically, the application of MIMO requires the estimation of radiopropagation channels between a single receiver and multipletransmitters. A conventional method to achieve this is to usepre-determined symbols known both to the transmitter and the receiver,herein called channel training symbols.

In IEEE 802.11ac, code orthogonal channel training symbols are used sothat the radio propagation channel specific to each transmitter (ortransmit stream) can be distinguished and estimated by simple flippingof sign and summation of received symbols. The summation of receivedsymbols allows the reduction of channel estimation error by reducing theeffects of random receiver noise. The advantage of the reduction ofchannel estimation error by this method is herein called the processinggain. However, this operation is effective only if the radio propagationchannels during the channel estimation period can be consideredstationary. In the case of IEEE 802.11ac, the maximum channel trainingperiod corresponds to 4 μsec×8=32 μs, and hence the method is expectedto work well as long as the variation of the radio propagation channelswithin 32 μs is small.

The same method may not be applicable when the symbol time becomeslonger and/or the variation of the radio channel within the channeltraining symbol time becomes larger, such as in the case of LTE-Advancedmobile standard, where one symbol time is 66.7 μs or longer. InLTE-Advanced mobile standard, the assumption of stationary channel overeight or more symbol time may not be valid. Alternatively, LTE-Advancedmobile standard defines the transmission of channel training symbol fromonly one transmitter within any one time-frequency slot. The radiopropagation channel can be estimated without interference from othertransmitters in this case. The advantage of this method is to be able tocope with a fast time varying channel. However, disadvantage of thismethod is the loss of processing gain to reduce the effects of receivernoise at the time of receiving the channel training symbols.

There is therefore a need to estimate the time varying channel formultiple of transmitters while taking advantage of processing gain aswell as being able to cope with a fast time varying channel.

The reference in this specification to any prior publication (orinformation derived from it), or to any matter which is known, is not,and should not be taken as an acknowledgment or admission or any form ofsuggestion that the prior publication (or information derived from it)or known matter forms part of the common general knowledge in the fieldof endeavour to which this specification relates.

SUMMARY

Disclosed are arrangements that estimate time-varying radio propagationchannel in the presence of multiple of transmitters operating at thesame radio frequency while achieving advantageous effects of processinggain.

In a first aspect there is provided a method of performingmulti-transmitter channel estimation for a time-varying channel, whereinthe method includes:

(a) wirelessly receiving at least two frames, each frame including ablock of training symbols received at different points in time for atime-varying channel;

(b) estimating, for each block at a block location, a first channelcoefficient of the time-varying channel, wherein the block location isthe same for each block; and

(c) interpolating or extrapolating a plurality of second channelcoefficients for the respective training symbols of each block based onthe respective first channel coefficient.

In certain embodiments of the first aspect, the method further includes:

(d) re-estimating the first channel coefficient for each block based onthe plurality of second channel coefficients for each block; and

(e) re-estimating the plurality of second channel coefficients for eachblock by interpolation or extrapolation using the respective firstchannel coefficient.

In certain embodiments of the first aspect, the method further includes

(f) iteratively performing steps (d) and (e) until the respectiveplurality of second channel coefficients for each block have converged,or until a specified number of iteration is reached.

In certain embodiments of the first aspect, a first channel coefficientfor each block is estimated in step (b) as being constant throughoutreception of the respective block.

In certain embodiments of the first aspect, the method is performed in atime domain.

In certain embodiments of the first aspect, the method is performed in afrequency domain.

In certain embodiments, the time-varying channel is a narrowbandcommunication channel, wherein the narrowband communication channel has:

a carrier frequency of 1 GHz or less; and

a bandwidth of 25 KHz or less.

In certain embodiments, the time-varying channel is a narrowbandcommunication channel, wherein the narrowband communication channel hasat least one of:

a carrier frequency of more than 1 GHz; and

a bandwidth of more than 25 KHz.

In certain embodiments, the time-varying channel is a widebandcommunication channel.

In a second aspect there is provided a receiver configured to performmulti-transmitter channel estimation for a time-varying channel, whereinthe receiver is configured to:

(a) wirelessly receive at least two frames, each frame including a blockof training symbols at different points in time for a time-varyingchannel;

(b) estimate, for each block at a block location, a first channelcoefficient of the time-varying channel, wherein the block location isthe same for each block; and

(c) interpolate or extrapolate a plurality of second channelcoefficients for the respective training symbols of each block based onthe respective first channel coefficient.

In certain embodiment of the second aspect, the receiver is furtherconfigured to:

(d) re-estimate the first channel coefficient for each block based onthe plurality of second channel coefficients for each block; and

(e) re-estimate the plurality of second channel coefficients for eachblock by interpolation or extrapolation using the respective firstchannel coefficient.

In certain embodiment of the second aspect, the receiver is configuredto iteratively re-estimate the first and second channel coefficients foreach block until convergence, or until a specified number of iterationis reached.

In certain embodiment of the second aspect, the receiver is configuredto estimate, for each block, the first channel coefficient as beingconstant throughout reception of the respective block.

In certain embodiments of the second aspect, the receiver is configuredto perform the multi-transmitter channel estimation in a time domain.

In certain embodiments of the second aspect, the receiver is configuredto perform the multi-transmitter channel estimation in a frequencydomain.

In certain embodiments, the time-varying channel is a narrowbandcommunication channel, wherein the narrowband communication channel has:

a carrier frequency of 1 GHz or less; and

a bandwidth of 25 KHz or less.

In certain embodiments, the time-varying channel is a narrowbandcommunication channel, wherein the narrowband communication channel hasat least one of:

a carrier frequency of more than 1 GHz; and

a bandwidth of more than 25 KHz.

In certain embodiments, the time-varying channel is a widebandcommunication channel.

In a third aspect there is provided a wireless communication systemincluding:

a plurality of transmitters, each transmitter transmitting in the samefrequency; and

a plurality of receivers, wherein each receiver is configured accordingto the second aspect.

In certain embodiment of the third aspect, each receiver is furtherconfigured to:

(d) re-estimate the first channel coefficient for each block based onthe plurality of second channel coefficients for each block; and

(e) re-estimate the plurality of second channel coefficients for eachblock by interpolation or extrapolation using the respective firstchannel coefficient.

In certain embodiment of the third aspect, each receiver is configuredto iteratively re-estimate the first and second channel coefficients foreach block until convergence, or until a specified number of iterationis reached.

In certain embodiment of the third aspect, each receiver is configuredto estimate, for each block, the first channel coefficient as beingconstant throughout reception of the respective block.

In certain embodiments of the third aspect, each receiver is configuredto perform the multi-transmitter channel estimation in a time domain.

In certain embodiments of the third aspect, each receiver is configuredto perform the multi-transmitter channel estimation in a frequencydomain.

In certain embodiments, the time-varying channel is a narrowbandcommunication channel, wherein the narrowband communication channel has:

a carrier frequency of 1 GHz or less; and

a bandwidth of 25 KHz or less.

In certain embodiments, the time-varying channel is a narrowbandcommunication channel, wherein the narrowband communication channel hasat least one of:

a carrier frequency of more than 1 GHz; and

a bandwidth of more than 25 KHz.

In certain embodiments, the time-varying channel is a widebandcommunication channel.

In a fourth aspect there is provided a computer readable mediumincluding executable instructions which, when executed by a processor ofa receiver, configure the receiver to perform multi-transmitter channelestimation for a time-varying channel, wherein the processor isconfigured to:

(a) wirelessly receive at least two frames, each frame including a blockof training symbols at different points in time for a time-varyingchannel;

(b) estimate, for each block at a block location, a first channelcoefficient of the time-varying channel, wherein the block location isthe same for each block; and

(c) interpolate or extrapolate a plurality of second channelcoefficients for the respective training symbols of each block based onthe respective first channel coefficient.

In certain embodiments of the fourth aspect, the receiver is furtherconfigured to:

(d) re-estimate the first channel coefficient for each block based onthe plurality of second channel coefficients for each block; and

(e) re-estimate the plurality of second channel coefficients for eachblock by interpolation or extrapolation using the respective firstchannel coefficient.

In certain embodiments of the fourth aspect, the receiver is configuredto iteratively re-estimate the first and second channel coefficients foreach block until convergence, or until a specified number of iterationsis reached.

In certain embodiments of the fourth aspect, the receiver is configuredto estimate, for each block, the first channel coefficient as beingconstant throughout reception of the respective block.

In certain embodiments of the fourth aspect, the receiver is configuredto perform the multi-transmitter channel estimation in a time domain.

In certain embodiments of the fourth aspect, the receiver is configuredto perform the multi-transmitter channel estimation in a frequencydomain.

In certain embodiments, the time-varying channel is a narrowbandcommunication channel, wherein the narrowband communication channel has:

a carrier frequency of 1 GHz or less; and

a bandwidth of 25 KHz or less.

In certain embodiments, the time-varying channel is a narrowbandcommunication channel, wherein the narrowband communication channel hasat least one of:

a carrier frequency of more than 1 GHz; and

a bandwidth of more than 25 KHz.

In certain embodiments, the time-varying channel is a widebandcommunication channel.

In a fifth aspect there is provided a multi-receiver device of awireless communication system for performing multi-transmitter channelestimation for a time-varying channel, wherein the multi-receiver deviceincludes a plurality of receivers, each receiver is configured toperform the method of the first aspect.

In a sixth aspect there is provided a system including:

a multi-transmitter device including a plurality of transmitters, eachtransmitter transmitting in the same frequency; and

a multi-receiver device configured according to the fifth aspect.

Other aspects and embodiments of the invention are also disclosed.

BRIEF DESCRIPTION OF THE PREFERRED EMBODIMENTS

Example embodiments should become apparent from the followingdescription, which is given by way of example only, of at least onepreferred but non-limiting embodiment, described in connection with theaccompanying figures.

FIG. 1a is a flowchart representing an example method of performingmulti-transmitter channel estimation for a time-varying channel;

FIG. 1b is a flowchart representing another example method of performingmulti-transmitter channel estimation for a time-varying channel;

FIG. 2 is a schematic illustrating a first channel estimation stage;

FIG. 3 is a schematic illustrating a second channel estimation stage;

FIG. 4 is an example of a schematic block diagram representation of asimulation performed using TDMA channel estimation, CDMA channelestimation, and the multi-transmitter channel estimation of the currentinvention;

FIG. 5 is an example low pass filter used for interpolation in thesecond channel estimation stage for the simulation;

FIG. 6 is a plot of simulation results of mean error vector magnitudeversus receiver SNR for TDMA channel estimation, CDMA channelestimation, and the multi-transmitter channel estimation of the currentinvention for the simulation of FIG. 4;

FIG. 7 is a plot of simulation results of bit error probability versusreceiver SNR for TDMA channel estimation, CDMA channel estimation, andthe multi-transmitter channel estimation of the current invention forthe simulation of FIG. 4; and

FIGS. 8a and 8b collectively form a schematic block diagramrepresentation of a receiver; and

FIG. 9 is a system diagram of a system including a multi-receiver deviceand a multi-transmitter device.

DETAILED DESCRIPTION

The following modes, given by way of example only, are described inorder to provide a more precise understanding of the subject matter of apreferred embodiment or embodiments. In the figures, incorporated toillustrate features of an example embodiment, like reference numeralsare used to identify like parts throughout the figures.

Referring to FIG. 1a there is shown a flowchart representing an examplemethod 100 of performing multi-transmitter channel estimation for atime-varying channel.

At step 110, the method 100 includes wirelessly receiving at least twoframes, each frame including a block of training symbols received atdifferent points in time for a time-varying channel.

At step 120, the method 100 includes estimating, for each block at ablock location, a first channel coefficient of the time-varying channel,wherein the block location is the same for each block.

At step 130, the method 100 includes interpolating or extrapolating aplurality of second channel coefficients for the respective trainingsymbols of each block based on the respective first channel coefficient.

Referring to FIG. 1b there is shown another example method 150 ofperforming multi-transmitter channel estimation for a time-varyingchannel.

In particular, at step 155 the method 150 includes wirelessly receivingat least two frames, each frame including a block of training symbolsreceived at different points in time for a time-varying channel.

At step 160, the method 150 includes estimating, for each block at ablock location, a first channel coefficient of the time-varying channel,wherein the block location is the same for each block. Preferably, thefirst channel coefficient for each block is estimated during step 160 asbeing constant throughout the reception of the respective block.

At step 165, the method 150 includes interpolating or extrapolating aplurality of second channel coefficients for the respective trainingsymbols of each block based on the respective first channel coefficient.

At step 170, the method includes re-estimating the first channelcoefficient for each block based on the plurality of second channelcoefficients for each block.

At step 175, the method includes re-estimating the plurality of secondchannel coefficients for each block by interpolation or extrapolationusing the respective first channel coefficient.

At step 180, the method includes determining if the plurality of secondchannel coefficients for each block have converged or a specified numberof iterations have been performed. In the event of a positivedetermination, channel estimation has been completed. In the event of anegative determination, the method proceeds back to step 170 to performanother iteration of steps 170, 175 and 180 until convergence isachieved, or until a specified number of iterations have been performed.

As will be appreciated from methods 100 and 150, channel estimation fora time-varying channel comprises of at least two stages of channelestimation. The first stage is to estimate a constant component of thechannel (i.e. the first channel coefficient) during the reception of atleast two blocks of channel training symbols, wherein the at least twoblocks are received at two different points in time. The second stage isto utilise the estimated constant component of the channel at thedifferent points in time to estimate the channel coefficients (i.e. thesecond channel coefficients) for the channel training symbols of eachblock by interpolation and/or extrapolation. As shown in FIG. 1B, thetwo stages may be repeated iteratively such that previous calculatedchannel coefficients can be used for re-estimating the first and secondchannel coefficients. Utilising interpolation or extrapolationpreferably reduces the error caused by inaccuracy in channel estimationby taking advantage of coherence of the channel in the time domain.

Referring to FIG. 2, there is shown an example structure of a symbolsequence transmitted from the transmitter (Tx1). In this example, thetransmitted symbol sequence includes two frames. Each frame includes achannel training symbol part P and a data part D.

During the initial stage of channel estimation, the first channelcoefficients at time F1 and F2, and possibly at other frame times, areinitially estimated by assuming that the channel is constant during thereception of channel training symbols. For example, initially thechannel is assumed to be constant during P11 and P12 for frame 1, andduring P21 and P22 for frame 2. As can be seen in FIG. 2, the locationwithin each block which each first channel coefficient is estimated isthe same, wherein in this particular instance F1 and F2 are bothlocation of the second training symbol for respective blocks.

FIG. 3 shows the second channel estimation stage. By using the estimatedfirst channel coefficients at F1 and F2, the second channel coefficientsat symbol times P11, P12, P21, and P22 are estimated by interpolatingand/or extrapolating the channel coefficients estimated for F1 and F2.Due to the coherence of the channel in time, theinterpolation/extrapolation step can take advantage of the availabilityof estimated channel coefficients at multiple points in time so that theaccuracy of the estimation of the channel corresponding to each of thechannel training symbols may be improved.

The process can then be repeated. In particular, the estimated secondchannel coefficients at P11, P12, P21 and P22 can be utilised tore-estimate the first channel coefficients at time F1 and F2. Then, thesecond channel coefficients at P11, P12, P21 and P22 can be re-estimatedtaking into account the re-estimated first channel coefficients at F1and F2, The process can be repeated iteratively to improve the accuracyof the channel estimation.

The method can be performed utilising a matrix that can be invertible inthe time domain and/or the frequency domain as will be explainedmathematically below. In particular, the received symbols at a receiveris given as:

${y\left( i_{z} \right)} = {{\sum\limits_{i_{T} = 1}^{N_{T}}{{h\left( {i_{T},i_{Z}} \right)} \times \left( {i_{T},i_{Z}} \right)}} + {n\left( i_{Z} \right)}}$

where i_(Z)=1, 2, . . . , N_(Z) and

-   -   y(i_(Z)) is the received symbol at the i_(Z)th symbol time,    -   h(i_(T), i_(Z)) is the single tap channel coefficient between        the i_(T)th transmitter and the receiver at the i_(Z)th symbol        time,    -   x(i_(T), i_(Z)) is the channel training symbol for the i_(T)th        transmitter at the i_(Z)th symbol time, and    -   n(i_(Z)) is the noise at the receiver at the i_(Z)th symbol        time.

The number of channel training symbols per a block is N_(Z).

Separating each of the channel coefficients into a constant portion anda time varying portion provides:

$\begin{matrix}{{y\left( i_{z} \right)} = {{\sum\limits_{i_{T} = 1}^{N_{T}}{{g\left( i_{T} \right)}{f\left( {i_{T},i_{Z}} \right)} \times \left( {i_{T},i_{Z}} \right)}} + {n\left( i_{Z} \right)}}} & (1)\end{matrix}$

where

h(i _(T) , i _(z))=g(i _(T))f(i _(T) , i _(z))   (2)

and

-   -   g(i) is the constant term of the single tap channel coefficient        between the i_(T)th transmitter and the receiver over the        duration of a block of channel training symbols, and    -   f(i_(T), i_(Z)) is the time varying part of the single tap        channel coefficient between the i_(T)th transmitter and the        receiver at the i_(Z)th symbol time.

The channel estimation may be performed in time domain or in frequencydomain.

For time domain channel estimation, the above equation can be written ina matrix form as the following:

$\begin{matrix}{\begin{bmatrix}{y(1)} \\\vdots \\{y\left( N_{Z} \right)}\end{bmatrix} = {{\begin{bmatrix}{w\left( {1,1} \right)} & \ldots & {w\left( {N_{T},1} \right)} \\\vdots & \ddots & \vdots \\{y\left( N_{Z} \right)} & \ldots & {w\left( {N_{T},N_{Z}} \right)}\end{bmatrix}\begin{bmatrix}{g(1)} \\\vdots \\{g\left( N_{T} \right)}\end{bmatrix}} + \begin{bmatrix}{n(1)} \\\vdots \\{n\left( N_{Z} \right)}\end{bmatrix}}} & (3)\end{matrix}$

where i_(Z)=1, 2, . . . , N_(Z) and w(i_(T), i_(Z))=f(i_(T),i_(Z))x(i_(T), i_(Z)).

As discussed above, the initial estimate of f(i_(T), i_(Z)) (herein{tilde over (f)}(i_(T), i_(Z), 1)) is assumed to be constant and isequal to:

{tilde over (f)}(i _(T) , i _(Z), 1)=1   (4)

Then the initial estimate of w(i_(T), i_(Z)) (herein {tilde over(w)}(i_(T), i_(Z), 1)) is defined as:

{tilde over (w)}(i _(T) , i _(Z), 1)={tilde over (f)}(i_(T) , i _(Z),1)x(i _(T) , i _(Z))=x(i _(T) , i _(Z))   (5)

Then the initial estimate of g(i_(T)) (herein {tilde over (g)}(i_(T),1)) can be obtained by:

$\begin{matrix}{\begin{bmatrix}{\overset{\sim}{g}\left( {1,1} \right)} \\\vdots \\{\overset{\sim}{g}\left( {N_{T},1} \right)}\end{bmatrix} = {{\begin{bmatrix}{\overset{\sim}{w}\left( {1,1,1} \right)} & \ldots & {\overset{\sim}{w}\left( {N_{T},1,1} \right)} \\\vdots & \ddots & \vdots \\{\overset{\sim}{w}\left( {1,N_{Z},1} \right)} & \ldots & {\overset{\sim}{w}\left( {N_{T},N_{Z},1} \right)}\end{bmatrix}^{- 1}\begin{bmatrix}{y(1)} \\\vdots \\{y\left( N_{Z} \right)}\end{bmatrix}} = {\begin{bmatrix}{x\left( {1,1} \right)} & \ldots & {x\left( {N_{T},1} \right)} \\\vdots & \ddots & \vdots \\{x\left( {1,N_{Z}} \right)} & \ldots & {x\left( {N_{T},N_{Z}} \right)}\end{bmatrix}^{- 1}\begin{bmatrix}{y(1)} \\\vdots \\{y\left( N_{Z} \right)}\end{bmatrix}}}} & (6)\end{matrix}$

The initial estimate of h(i_(T), i_(Y)) (herein {tilde over (h)}(i_(T),i_(Y), 1)), where i_(Y) represents the representative time (e.g. in themiddle of the block of the channel training symbols) for thecorresponding channel training symbol period, is defined as:

{tilde over (h)}(i _(T) , i _(Y), 1)={tilde over (g)}(i _(T), 1)   (7)

The initial estimation of {tilde over (h)}(i_(T), i_(Z), 1), is obtainedby interpolating or extrapolating {tilde over (h)}(i_(T), i_(y), 1)obtained at two or more frames.

As the constant part of the channel is assumed to be equal to 1, there-estimate of the time varying part of the single tap channelcoefficients (i.e. {tilde over (f)}(i_(T), i_(z), 2)) is:

{tilde over (f)}(i _(T) , i _(Z), 2)={tilde over (h)}(i _(T) , i_(Z), 1)   (8)

The updated second estimate of w(i_(T), i_(Z)) (i.e. {tilde over(w)}(i_(T), i_(Z), 2)) is defined as:

{tilde over (w)}(i _(T) , i _(Z), 2)={tilde over (f)}(i _(T) , i _(Z),2)x(i _(T) , i _(Z))   (9)

The update of the estimation of g(i_(T)) can be further performed by:

$\begin{matrix}{\begin{bmatrix}{\overset{\sim}{g}\left( {1,2} \right)} \\\vdots \\{\overset{\sim}{g}\left( {N_{T},2} \right)}\end{bmatrix} = {\begin{bmatrix}{\overset{\sim}{w}\left( {1,1,2} \right)} & \ldots & {\overset{\sim}{w}\left( {N_{T},1,2} \right)} \\\vdots & \ddots & \vdots \\{\overset{\sim}{w}\left( {1,N_{Z},2} \right)} & \ldots & {\overset{\sim}{w}\left( {N_{T},N_{Z},2} \right)}\end{bmatrix}^{- 1}\begin{bmatrix}{y(1)} \\\vdots \\{y\left( N_{Z} \right)}\end{bmatrix}}} & (10)\end{matrix}$

The process can be performed iteratively until the results converge, oruntil a specified number of iteration is reached.

The process can be also performed in frequency domain. In particular,the Fourier transform of the received symbols can be given by

$\begin{matrix}{{Y\left( i_{F} \right)} = {{\sum\limits_{i_{Z} = 1}^{N_{Z}}{{y\left( i_{Z} \right)}e^{- \frac{j\; 2\; {\pi {({i_{Z} - 1})}}{({i_{F} - 1})}}{N_{Z}}}}} = {{\sum\limits_{i_{T} = 1}^{N_{T}}{{g\left( i_{T} \right)}{W\left( {i_{T},i_{F}} \right)}}} + {N\left( i_{F} \right)}}}} & (11)\end{matrix}$

where i_(F)=1, 2, . . . , N_(F) and

-   -   Y(i_(F)) is the Fourier transform of y(i_(Z)),    -   W(i_(T), i_(F)) is the Fourier transform off (i_(T),        i_(Z))x(i_(T), i_(Z)), and    -   N(i_(F)) is the Fourier transform of n(i_(z)).

The above equation can be written in a matrix form as the following:

$\begin{matrix}{\begin{bmatrix}{Y(1)} \\\vdots \\{Y\left( N_{F} \right)}\end{bmatrix} = {{\begin{bmatrix}{W\left( {1,1} \right)} & \ldots & {W\left( {N_{T},1} \right)} \\\vdots & \ddots & \vdots \\{W\left( {1,N_{F}} \right)} & \ldots & {W\left( {N_{T},N_{F}} \right)}\end{bmatrix}\begin{bmatrix}{g(1)} \\\vdots \\{g\left( N_{T} \right)}\end{bmatrix}} + \begin{bmatrix}{N(1)} \\\vdots \\{N\left( N_{F} \right)}\end{bmatrix}}} & (12)\end{matrix}$

Again, the initial estimate of f(i_(T), i_(Z))(i.e. {tilde over(f)}(i_(T), i_(Z), 1)) is:

{tilde over (f)}(i _(T) , i _(Z), 1)=1   (13)

Then the initial estimate of W(i_(T), i_(F)) (herein {tilde over(W)}(i_(T), i_(F), 1)) is given as the Fourier transform of:

{tilde over (w)}(i _(T) , i _(Z), 1)={tilde over (f)}(i _(T) , i _(Z),1)x(i _(T) , i _(Z))=x(i _(T) , i _(Z))   (14)

Then the initial estimate of g(i_(T)), {tilde over (g)}(i_(T), 1), canbe obtained by:

$\begin{matrix}{\begin{bmatrix}{\overset{\sim}{g}\left( {1,1} \right)} \\\vdots \\{\overset{\sim}{g}\left( {N_{T},1} \right)}\end{bmatrix} = {{\begin{bmatrix}{\overset{\sim}{W}\left( {1,1,1} \right)} & \ldots & {\overset{\sim}{W}\left( {N_{T},1,1} \right)} \\\vdots & \ddots & \vdots \\{\overset{\sim}{W}\left( {1,N_{F},1} \right)} & \ldots & {\overset{\sim}{W}\left( {N_{T},N_{F},1} \right)}\end{bmatrix}^{- 1}\begin{bmatrix}{Y(1)} \\\vdots \\{Y\left( N_{F} \right)}\end{bmatrix}} = {\begin{bmatrix}{X\left( {1,1} \right)} & \ldots & {X\left( {N_{T},1} \right)} \\\vdots & \ddots & \vdots \\{X\left( {1,N_{F}} \right)} & \ldots & {X\left( {N_{T},N_{F}} \right)}\end{bmatrix}^{- 1}\begin{bmatrix}{Y(1)} \\\vdots \\{Y\left( N_{F} \right)}\end{bmatrix}}}} & (15)\end{matrix}$

A similar process to that which occurred in the time domain follows toobtain the next updated estimate of g(i_(T)), namely {tilde over(g)}(i_(T),2). The process can be performed iteratively until theresults converge, or until a specified number of iterations have beenperformed.

Simulation

A set of computer simulations were performed to demonstrate theeffectiveness of the channel estimation method for a multi-transmittertime varying channel.

As an example, the simulation was configured to use four transmittersand eight receivers to perform a 4×8 MIMO wireless transmission in asingle carrier. The simulation was performed on the baseband.Independent and identically distributed (i.i.d.) Rayleigh frequency flattime varying fading channel model with the maximum Doppler frequency of200 Hz was used as an example.

Three channel estimation methods were compared:

-   -   LTE-Advanced like time division multi-transmitter method denoted        as TDMT channel estimation.    -   IEEE 802.11ac like code division multi-transmitter channel        estimation method denoted as CDMT channel estimation.    -   Channel estimation using the current invention, denoted as        iterative multi-transmitter (IMT) channel estimation.

The channel training symbols for the above three methods are as follows:

-   -   TDMT:        -   [1 0 0 0] for transmitter 1,        -   [0 1 0 0] for transmitter 2,        -   [0 0 1 0] for transmitter 3, and        -   [0 0 0 1] for transmitter 4.    -   CDMT:        -   [1 -1 1 1] for transmitter 1,        -   [1 1 -1 1] for transmitter 2,        -   [1 1 1 -1] for transmitter 3, and        -   [−1 1 1 1] for transmitter 4.    -   IMT: as shown in Table 1.

TABLE 1 Example IMT channel training symbols for four transmitters.Symbol 1 Symbol 2 Symbol 3 Symbol 4 Real Imag Real Imag Real Imag RealImag Transmitter 1 −0.2555 0.6382 −0.1588 0.4206 1.4437 0.1427 1.09090.3107 Transmitter 2 0.1879 0.5890 −0.2478 −0.6372 −0.9254 0.6894 1.2218−0.6259 Transmitter 3 0.8532 0.6171 1.5072 0.2400 0.0315 0.7085 −0.24190.2573 Transmitter 4 −1.4181 0.3022 0.7898 −0.6657 0.3256 0.1435 −0.3590−0.8007

The simulation process 400 is depicted in the block diagram shown inFIG. 4. In particular, an information bit generator module 410 for eachof the four transmitters, Tx1 to Tx4, generates random binaryinformation bits. A set of eight consecutive information bits from theoutput of the information bit generator module 410 is converted into oneof 256 quadrature amplitude modulation (QAM) data symbols by a 256QAMmapper module 420. A set of twelve consecutive 256QAM data symbols arepre-fixed with four channel training symbols, generated by a channeltraining symbol generator 440, by a frame assembler module 430. Theoutput of the frame assembler module 430 is fed into the basebandchannel simulator module 450.

As an example, a symbol duration of 72 μs was chosen, which is similarto LTE-Advanced symbol duration. With sixteen symbols per frame, theduration of a frame is 1152 μs in this example. The ratio of the numberof channel training symbols to the number of data symbols in each frameis determined so that the channel coefficients can be estimatedfrequently enough to capture the temporal variation of the radiopropagation channel. As a rule of thumb, the maximum Doppler frequencyof 200 Hz requires the estimation of the channel at the ratecorresponding to 400 Hz, which corresponds to the frame size of1/400=2.5 ms. The chosen frame duration of 1152 μs is expected tocapture the temporal variation of the channel well.

As previously mentioned, the channel simulator is configured to simulatefour transmitter—eight receiver MIMO i.i.d. Rayleigh frequency flat timevarying channel with the maximum Doppler frequency of 200 Hz. Thismaximum Doppler frequency corresponds to a movement of the transmittersTx1-Tx4 at approximately 108 km/h at a carrier frequency of 2 GHz.

At each of the eight receivers, the received stream of symbols arede-assembled by a frame de-assembler module 460 to extract the receivedsymbols corresponding to the channel training symbols and data symbols.The channel training symbol part of the received symbols are sent to thechannel estimation module 470 to estimate the channel at every datasymbol time.

For each channel estimation method, the same low pass filter basedinterpolation was used to derive channel coefficients at each datasymbol and in the case of IMT, the channel coefficients at the channeltraining symbols. The low pass filter was designed so that

-   -   The variation of the channel will not be blocked;    -   Noise or channel estimation error components may be blocked; and    -   The low pass filter amplitude decreases smoothly to zero at the        two edges.

For this example, the low pass filter, p(n), was defined as follows:

${p(n)} = {\frac{\sin \left( {\pi \; a} \right)}{\pi \; a}B_{209}}$where $a = {\frac{n}{16} - 6.5625}$

and n=1, . . . , 209. B₂₀₉ is a 209-point symmetric 4-termBlackman-Harris window. FIG. 5 shows a plot of the low pass filtercoefficients.

The output of the channel estimation module 470 and the received symbolscorresponding to the data symbol time are sent to zero-forcing (ZF)equaliser 480 to perform MIMO zero-forcing to produce estimatedtransmitted data symbols. The output of the ZF equaliser 480 is fed intoa 256QAM de-mapper module 490 to convert each of the estimated 256QAMdata symbols to corresponding binary bits. The original transmittedinformation bits are compared with the estimated information bits todetermine the bit error probability at an information bit sink module495. The absolute difference of the transmitted 256QAM data symbols andestimated 256QAM data symbols is known as the error vector magnitude(EVM).

FIGS. 6 and 7 show the simulation results in terms of mean EVM and biterror probability, respectively, as a function of receiver signal tonoise ratio (SNR). When the effects of receiver noise are larger thanthe variation of the channel during the four channel training symboltime (say the receiver SNR range from 10 dB to 15 dB), both the CDMT andIMT outperforming the TDMT method. This is due to CDMT and IMT usingfour channel training symbols to reduce the effects of receiver noise(i.e. processing gain) compared to TDMT which uses only one channeltraining symbol per transmitter. While the performance of TDMT may beimproved by allowing a higher power during the transmission of thechannel training symbols, such method would incur extra constraints insuch a component as a power amplifier and may not be practical.

As the receiver SNR increases, the effects of channel time variationsurpasses the effects of receiver noise and CDMT cannot take advantageof the higher receiver SNR and performance saturation is observed. Theperformance of both TDMT and IMT improves as the receiver SNR improves,with IMT outperforming TDMT by approximately 4 dB. Higher performanceimprovements are expected in relation to IMT when a larger number oftransmitters are involved due to a larger number of channel trainingsymbols per frame being required.

The above-described method is applicable to a system with multipletransmitters co-located or distributed, or a set of transmitters with asingle local oscillator or multiple local oscillators.

Referring to FIG. 9 there is shown a system diagram of a system 900utilising the multi-transmitter channel estimation method discussedabove. In particular the system 900 includes a plurality of trasmitters(Tx1 . . . TxN, collectively referred to as 910) and a plurality ofreceivers (Rx1 . . . RxN, collectively referred to as 920). Eachtransmitter Tx transmits in the same frequency as the remainingtransmitters. The system 900 can include a multi-transmitter device 905including the plurality of transmitters 910 and a multi-receiver device915 which includes the plurality of receivers 920. Each receiver Rx isconfigured to perform the method as described above. In particular, eachreceiver Rx can be configured to: (a) wirelessly receive at least twoframes, each frame including a block of training symbols received atdifferent points in time for a time-varying channel; (b) estimate, foreach block at a block location, a first channel coefficient of thetime-varying channel, wherein the block location is the same for eachblock; and (c) interpolate or extrapolate a plurality of second channelcoefficients for the respective training symbols of each block based onthe respective first channel coefficient.

In one particular embodiment, each receiver Rx may be a USRP (UniversalSoftware Radio Peripheral) device available from National Instruments.

It will be appreciated that as the method may be implemented by asoftware defined radio device, computer executable instructions may bestored in memory of the software defined radio device. In particular,the software defined radio device can include a non-transitory computerreadable medium including executable instructions which, when executedby a processor of the software defined radio device, configure thesoftware defined radio device to: (a) wirelessly receive at least twoframes, each frame including a block of training symbols received atdifferent points in time for a time-varying channel; (b) estimate, foreach block at a block location, a first channel coefficient of thetime-varying channel, wherein the block location is the same for eachblock; and (c) interpolate or extrapolate a plurality of second channelcoefficients for the respective training symbols of each block based onthe respective first channel coefficient. In certain embodiments, thesoftware defined radio device is further configured by execution of theexecutable instructions to: (d) re-estimate the first channelcoefficient for each block based on the plurality of second channelcoefficients for each block; and (e) re-estimate the plurality of secondchannel coefficients for each block by interpolation or extrapolationusing the respective first channel coefficient. Furthermore, thesoftware defined radio device is further configured by execution of theexecutable instructions to: (f) iteratively perform steps (d) and (e)until the respective plurality of second channel coefficients for eachblock have converged, or until a specified number of iterations arereached. In certain embodiments, a first channel coefficient for eachblock is estimated in step (b) as being constant throughout thereception of the respective block. In certain embodiments, the softwaredefined radio device performs the method in a time domain or a frequencydomain.

FIGS. 8a and 8b collectively form a schematic block diagram of a generalpurpose electronic device 801 including embedded components, in which achannel estimation processing module may be implemented. The channelestimation processing module may alternatively be implemented indedicated hardware such as one or more integrated circuits performingthe functions or sub functions of the channel estimation processingmodule. Such dedicated hardware may include graphic processors, digitalsignal processors, or one or more microprocessors and associatedmemories.

As seen in FIG. 8a , the electronic device 801 comprises an embeddedcontroller 802. Accordingly, the electronic device 801 may be referredto as an “embedded device.” In the present example, the controller 802has a processing unit (or processor) 805 which is bi-directionallycoupled to an internal storage module 809. The storage module 809 may beformed from non-volatile semiconductor read only memory (ROM) 860 andsemiconductor random access memory (RAM) 870, as seen in FIG. 8b . TheRAM 870 may be volatile, non-volatile or a combination of volatile andnon-volatile memory.

As seen in FIG. 8a , the electronic device 801 also comprises a portablememory interface 806, which is coupled to the processor 805 via aconnection 819. The portable memory interface 806 allows a complementaryportable memory device 825 to be coupled to the electronic device 801 toact as a source or destination of data or to supplement the internalstorage module 809. Examples of such interfaces permit coupling withportable memory devices such as Universal Serial Bus (USB) memorydevices, Secure Digital (SD) cards, Personal Computer Memory CardInternational Association (PCMIA) cards, optical disks and magneticdisks.

The electronic device 801 also has a communications interface 808 topermit coupling of the electronic device 801 to a computer orcommunications network 820 via a connection 821. The connection 821 maybe wired or wireless. For example, the connection 821 may be radiofrequency or optical. An example of a wired connection includesEthernet. Further, an example of wireless connection includes Bluetoothtype local interconnection, Wi-Fi (including protocols based on thestandards of the IEEE 802.11 family), Infrared Data Association (IrDa)and the like.

The method of FIGS. 1A and 1B may be implemented as one or more softwareapplication programs 833 executable within the embedded controller 802.In particular, with reference to FIG. 8b , the steps of the describedmethod are effected by instructions in the software 833 that are carriedout within the embedded controller 802. The software instructions may beformed as one or more code modules, each for performing one or moreparticular tasks.

The software 833 of the embedded controller 802 is typically stored inthe non-volatile ROM 860 of the internal storage module 809. Thesoftware 833 stored in the ROM 860 can be updated when required from acomputer readable medium. The software 833 can be loaded into andexecuted by the processor 805. In some instances, the processor 805 mayexecute software instructions that are located in RAM 870. Softwareinstructions may be loaded into the RAM 870 by the processor 805initiating a copy of one or more code modules from ROM 860 into RAM 870.Alternatively, the software instructions of one or more code modules maybe pre-installed in a non-volatile region of RAM 870 by a manufacturer.After one or more code modules have been located in RAM 870, theprocessor 805 may execute software instructions of the one or more codemodules.

The application program 833 is typically pre-installed and stored in theROM 860 by a manufacturer, prior to distribution of the electronicdevice 801. However, in some instances, the application programs 833 maybe supplied to the user encoded on one or more computer readable storagemedia 825 and read via the portable memory interface 806 of FIG. 8aprior to storage in the internal storage module 809. In anotheralternative, the software application program 833 may be read by theprocessor 805 from the network 820. Computer readable storage mediarefers to any non-transitory, tangible storage medium that participatesin providing instructions and/or data to the embedded controller 802 forexecution and/or processing. Examples of such storage media includefloppy disks, magnetic tape, CD-ROM, a hard disk drive, a ROM orintegrated circuit, USB memory, a magneto-optical disk, flash memory, ora computer readable card such as a PCMCIA card and the like, whether ornot such devices are internal or external of the electronic device 801.Examples of computer readable transmission media that may alsoparticipate in the provision of software, application programs,instructions and/or data to the electronic device 801 include radio orinfra-red transmission channels as well as a network connection toanother computer or networked device, and the Internet or Intranetsincluding e-mail transmissions and information recorded on Websites andthe like. A computer readable medium having such software or computerprogram recorded on it is a computer program product.

FIG. 8b illustrates in detail the embedded controller 802 having theprocessor 805 for executing the application programs 833 and theinternal storage 809. The internal storage 809 comprises read onlymemory (ROM) 860 and random access memory (RAM) 870. The processor 805is able to execute the application programs 833 stored in one or both ofthe connected memories 860 and 870. When the electronic device 801 isinitially powered up, a system program resident in the ROM 860 isexecuted. The application program 833 permanently stored in the ROM 860is sometimes referred to as “firmware”. Execution of the firmware by theprocessor 805 may fulfil various functions, including processormanagement, memory management, device management, storage management anduser interface.

The processor 805 typically includes a number of functional modulesincluding a control unit (CU) 851, an arithmetic logic unit (ALU) 852and a local or internal memory comprising a set of registers 854 whichtypically contain atomic data elements 856, 857, along with internalbuffer or cache memory 855. One or more internal buses 859 interconnectthese functional modules. The processor 805 typically also has one ormore interfaces 858 for communicating with external devices via systembus 881 , using a connection 861.

The application program 833 includes a sequence of instructions 862though 863 that may include conditional branch and loop instructions.The program 833 may also include data, which is used in execution of theprogram 833. This data may be stored as part of the instruction or in aseparate location 864 within the ROM 860 or RAM 870.

In general, the processor 805 is given a set of instructions, which areexecuted therein. This set of instructions may be organised into blocks,which perform specific tasks or handle specific events that occur in theelectronic device 801. Typically, the application program 833 waits forevents and subsequently executes the block of code associated with thatevent. Events may be triggered in response to input from a user, via theuser input devices 813 of FIG. 8 a, as detected by the processor 805.Events may also be triggered in response to other sensors and interfacesin the electronic device 801.

The execution of a set of the instructions may require numeric variablesto be read and modified. Such numeric variables are stored in the RAM870. The disclosed method uses input variables 871 that are stored inknown locations 872, 873 in the memory 870. The input variables 871 areprocessed to produce output variables 877 that are stored in knownlocations 878, 879 in the memory 870. Intermediate variables 874 may bestored in additional memory locations in locations 875, 876 of thememory 870. Alternatively, some intermediate variables may only exist inthe registers 854 of the processor 805.

The execution of a sequence of instructions is achieved in the processor805 by repeated application of a fetch-execute cycle. The control unit851 of the processor 805 maintains a register called the programcounter, which contains the address in ROM 860 or RAM 870 of the nextinstruction to be executed. At the start of the fetch execute cycle, thecontents of the memory address indexed by the program counter is loadedinto the control unit 851. The instruction thus loaded controls thesubsequent operation of the processor 805, causing for example, data tobe loaded from ROM memory 860 into processor registers 854, the contentsof a register to be arithmetically combined with the contents of anotherregister the contents of a register to be written to the location storedin another register and so on. At the end of the fetch execute cycle theprogram counter is updated to point to the next instruction in thesystem program code. Depending on the instruction just executed this mayinvolve incrementing the address contained in the program counter orloading the program counter with a new address in order to achieve abranch operation.

Each step or sub-process in the method of FIGS. 1a and 1b is associatedwith one or more segments of the application program 833, and isperformed by repeated execution of a fetch-execute cycle in theprocessor 805 or similar programmatic operation of other independentprocessor blocks in the electronic device 801.

The arrangements described are applicable to the wireless communicationindustries.

In one form, the time-varying channel can be a narrowband communicationchannel of a mobile environment. For example, the narrowbandcommunication channel can have a carrier frequency of 1 GHz or less. Inanother form, the narrowband communication channel can have a bandwidthof 25 KHz or less. In another example, the narrowband communicationchannel can have a carrier frequency of 1 GHz or less and a bandwidth of25 KHz or less.

Alternatively, the time-varying channel can be a narrowbandcommunication channel of a mobile environment with othercharacteristics. For example, the time-varying channel can be anarrowband communication channel of a mobile environment having acarrier frequency greater than 1 GHz. In another form, the time-varyingchannel can be a narrowband communication channel of a mobileenvironment having a bandwidth of more than 25 KHz. In another form, thetime-varying channel can be a narrowband communication channel of amobile environment having a carrier frequency greater than 1 GHz and abandwidth of more than 25 KHz.

In a further alternative, the time-varying channel can be a widebandcommunication channel of a mobile environment.

Many modifications will be apparent to those skilled in the art withoutdeparting from the scope of the present invention.

The claims of the present invention are as follows:
 1. A method ofperforming multi-transmitter channel estimation for a time-varyingchannel, wherein the method includes: (a) wirelessly receiving at leasttwo frames, each frame including a block of training symbols received atdifferent points in time for a time-varying channel; (b) estimating, foreach block at a block location, a first channel coefficient of thetime-varying channel, wherein the block location is the same for eachblock; and (c) interpolating or extrapolating a plurality of secondchannel coefficients for the respective training symbols of each blockbased on the respective first channel coefficient.
 2. The methodaccording to claim 1, wherein the method further includes: (d)re-estimating the first channel coefficient for each block based on theplurality of second channel coefficients for each block; and (e)re-estimating the plurality of second channel coefficients for eachblock by interpolation or extrapolation using the respective firstchannel coefficient.
 3. The method according to claim 2, wherein themethod further includes (f) iteratively performing steps (d) and (e)until the respective plurality of second channel coefficients for eachblock have converged, or until a specified number of iterations isreached.
 4. The method according to any one of claims 1 to 3, wherein afirst channel coefficient for each block is estimated in step (b) asbeing constant throughout reception of the respective block.
 5. Themethod according to any one of claims 1 to 4, wherein the method isperformed in a time domain.
 6. The method according to any one of claims1 to 4, wherein the method is performed in a frequency domain.
 7. Themethod according to any one of claims 1 to 6, wherein the time-varyingchannel is a narrowband communication channel, wherein the narrowbandcommunication channel has: a carrier frequency of 1 GHz or less; and abandwidth of 25 KHz or less.
 8. The method according to any one ofclaims 1 to 6, wherein the time-varying channel is a narrowbandcommunication channel, wherein the narrowband communication channel hasat least one of: a carrier frequency of more than 1 GHz; and a bandwidthof more than 25 KHz.
 9. The method according to any one of claims 1 to6, wherein the time-varying channel is a wideband communication channel.10. A receiver configured to perform multi-transmitter channelestimation for a time-varying channel, wherein the receiver isconfigured to: (a) wirelessly receive at least two frames, each frameincluding a block of training symbols at different points in time for atime-varying channel; (b) estimate, for each block at a block location,a first channel coefficient of the time-varying channel, wherein theblock location is the same for each block; and (c) interpolate orextrapolate a plurality of second channel coefficients for therespective training symbols of each block based on the respective firstchannel coefficient.
 11. The receiver according to claim 10, wherein thereceiver is further configured to: (d) re-estimate the first channelcoefficient for each block based on the plurality of second channelcoefficients for each block; and (e) re-estimate the plurality of secondchannel coefficients for each block by interpolation or extrapolationusing the respective first channel coefficient.
 12. The receiveraccording to claim 11, wherein the receiver is configured to iterativelyre-estimate the first and second channel coefficients for each blockuntil convergence, or until a specified number of iterations is reached.13. The receiver according to any one of claims 10 to 12, wherein thereceiver is configured to estimate, for each block, the first channelcoefficient as being constant throughout reception of the respectiveblock.
 14. The receiver according to any one of claims 10 to 13, whereinthe receiver is configured to perform the multi-transmitter channelestimation in a time domain.
 15. The receiver according to any one ofclaims 10 to 14, wherein the receiver is configured to perform themulti-transmitter channel estimation in a frequency domain.
 16. Thereceiver according to any one of claims 10 to 15, wherein thetime-varying channel is a narrowband communication channel, wherein thenarrowband communication channel has: a carrier frequency of 1 GHz orless; and a bandwidth of 25 KHz or less.
 17. The receiver according toany one of claims 10 to 15, wherein the time-varying channel is anarrowband communication channel, wherein the narrowband communicationchannel has at least one of: a carrier frequency of more than 1 GHz; anda bandwidth of more than 25 KHz.
 18. The receiver according to any oneof claims 10 to 15, wherein the time-varying channel is a widebandcommunication channel.
 19. A wireless communication system including: aplurality of transmitters, each transmitter transmitting in the samefrequency; and a plurality of receivers, wherein each receiver isconfigured according to any one of claims 10 to
 18. 20. A computerreadable medium including executable instructions which, when executedby a processor of a receiver, configure the receiver to performmulti-transmitter channel estimation for a time-varying channel, whereinthe processor is configured to: (a) wirelessly receive at least twoframes, each frame including a block of training symbols at differentpoints in time for a time-varying channel; (b) estimate, for each blockat a block location, a first channel coefficient of the time-varyingchannel, wherein the block location is the same for each block; and (c)interpolate or extrapolate a plurality of second channel coefficientsfor the respective training symbols of each block based on therespective first channel coefficient.
 21. The computer readable mediumaccording to claim 20, wherein the receiver is further configured to:(d) re-estimate the first channel coefficient for each block based onthe plurality of second channel coefficients for each block; and (e)re-estimate the plurality of second channel coefficients for each blockby interpolation or extrapolation using the respective first channelcoefficient.
 22. The computer readable medium according to claim 21,wherein the receiver is configured to iteratively re-estimate the firstand second channel coefficients for each block until convergence, oruntil a specified number of iterations is reached.
 23. The computerreadable medium according to any one of claims 20 to 22, wherein thereceiver is configured to estimate, for each block, the first channelcoefficient as being constant throughout reception of the respectiveblock.
 24. The computer readable medium according to any one of claims20 to 23, wherein the receiver is configured to perform themulti-transmitter channel estimation in a time domain.
 25. The computerreadable medium according to any one of claims 20 to 24, wherein thereceiver is configured to perform the multi-transmitter channelestimation in a frequency domain.
 26. The computer readable mediumaccording to any one of claims 20 to 25, wherein the time-varyingchannel is a narrowband communication channel, wherein the narrowbandcommunication channel has: a carrier frequency of 1 GHz or less; and abandwidth of 25 KHz or less.
 27. The computer readable medium accordingto any one of claims 20 to 25, wherein the time-varying channel is anarrowband communication channel, wherein the narrowband communicationchannel has at least one of: a carrier frequency of more than 1 GHz; anda bandwidth of more than 25 KHz.
 28. The receiver according to any oneof claims 20 to 25, wherein the time-varying channel is a widebandcommunication channel.
 29. A multi-receiver device of a wirelesscommunication system for performing multi-transmitter channel estimationfor a time-varying channel, wherein the multi-receiver device includes aplurality of receivers, each receiver is configured to perform themethod of any one of claims 1 to
 9. 30. A system including: amulti-transmitter device including a plurality of transmitters, eachtransmitter transmitting in the same frequency; and a multi-receiverdevice configured according to claim 29.